ScalarProduct[p, q]
is the input for the scalar product of two Lorentz vectors p and q.
ScalarProduct[p] is equivalent to ScalarProduct[p, p].
Expansion of sums of momenta in ScalarProduct
is done with ExpandScalarProduct
.
Scalar products may be set, e.g. via ScalarProduct[a, b] = m^2
; but a
and b
may not contain sums.
ScalarProduct[a]
corresponds to ScalarProduct[a,a]
Note that ScalarProduct[a, b] = m^2
actually sets Lorentzian scalar products in different dimensions specified by the value of the SetDimensions
option.
It is highly recommended to set ScalarProduct
s before any calculation. This improves the performance of FeynCalc.
Overview, Calc, FCClearScalarProducts, ExpandScalarProduct, ScalarProductCancel, Pair, SP, SPD.
[p, q] ScalarProduct
[p + q, -q] ScalarProduct
[p, p] ScalarProduct
[q] ScalarProduct
[p, q] // StandardForm
ScalarProduct
(*Pair[Momentum[p], Momentum[q]]*)
[p, q, Dimension -> D] // StandardForm
ScalarProduct
(*Pair[Momentum[p, D], Momentum[q, D]]*)
[Subscript[p, 1], Subscript[p, 2]] = s/2 ScalarProduct
[ ScalarProduct[Subscript[p, 1] - q, Subscript[p, 2] - k]] ExpandScalarProduct
[ ScalarProduct[Subscript[p, 1] - q, Subscript[p, 2] - k]] Calc
[q1] = qq; ScalarProduct
[q1] SP
[] FCClearScalarProducts